the compact finite difference schemes have been found to give simple ways of reaching the objectives of high accuracy and low computational cost. during the past two decades, the compact schemes have been used extensively for numerical simulation of various fluid dynamics problems. these methods have also been applied for numerical solution of some prototype geophysical fluid dynamics problems ...

Numerical simulation of advective-dispersive contaminant transport is carried out by using high-order compact finite difference schemes combined with second-order MacCormack and fourth-order Runge-Kutta schemes. Both of the two schemes have accuracy of sixth-order in space. A sixth-order MacCormack scheme is proposed for the first time within this study. For the aim of demonstrating efficiency ...

We study the numerical anisotropy existent in compact difference schemes as applied to hyperbolic partial differential equations, and propose an approach to reduce this error and to improve the stability restrictions based on a previous analysis applied to explicit schemes. A prefactorization of compact schemes is applied to avoid the inversion of a large matrix when calculating the derivatives...

In this work, a predictor–corrector compact difference scheme for nonlinear fractional differential equation is presented. The MacCormack method provided to deal with terms, the Riemann–Liouville (R-L) integral term treated by means of second-order convolution quadrature formula, and Caputo derivative discretized L1 discrete formula. Through first second derivatives matrix under difference, we ...

We study the numerical anisotropy existent in compact difference schemes as applied to hyperbolic partial differential equations, and propose an approach to reduce this error and to improve the stability restrictions based on a previous analysis applied to explicit schemes. A prefactorization of compact schemes is applied to avoid the inversion of a large matrix when calculating the derivatives...

The back and forth error compensation and correction (BFECC) method advects the solution forward and then backward in time. The result is compared to the original data to estimate the error. Although inappropriate for parabolic and other nonreversible partial differential equations, it is useful for often troublesome advection terms. The error estimate is used to correct the data before advecti...

this work reports the results of the application of the second-order maccormack method for numerical solution of‎ the conservative form of two-dimensional non-hydrostatic and fully compressible navier-stokes equations governing an inviscid and adiabatic atmosphere‎. various aspects of the computational approach such as discretization of the governing equations for the interior and boundary poin...

A numerical method based on the MacCormack finite difference scheme is presented. The method was developed for simulating two-dimensional overland flow with spatially variable infiltration and microtopography using the hydrodynamic flow equations. The basic MacCormack scheme is enhanced by using the method of fractional steps to simplify application; treating the friction slope, a stiff source ...

The offer made by tlie President of the lloyal College of Surgeons to proceed to the Cape in the capacity of Consulting Surgeon has been accepted by Government with graceful alacrity; and, after a very hearty "send off" at Waterloo by the students of St. Thomas's Hospital and probably other schools, Sir William proceeded from Southampton by the Union liner Breton. He is to be associated in his ...